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Small-scale Structure via Flows
[chapter]
2004
Fractal Geometry and Stochastics III
We study the small scale of geometric objects embedded in a Euclidean space by means of the flow defined by zooming toward a point of the space. For a smooth embedded manifold one sees just the tangent space asymptotically, but for fractal sets and related objects (space-filling curves, nested tilings) the flow can be quite interesting, as the "scenery" one sees keeps changing. For a Kleinian limit set the scenery flow and geodesic flows are isomorphic. This fact suggests that for a Julia set
doi:10.1007/978-3-0348-7891-3_4
fatcat:zzx5uizvaffn7mggvadnue4tem